The local authority is consulting parents and schools on boundaries for a two-form entry school which would be built on at The Westgate secondary school.
The new catchment area will come into force when the primary opens to reception pupils in September 2014 and becomes the first county-run school for pupils aged four to 16.
Under the new proposals, a child living in the St Bede catchment area would be within the boundaries of both St Bede and Westgate.
Similarly, a child living within the Western catchment area would be in catchment areas for both Western and Westgate.
County chiefs say the shared catchment approach is intended to make it easier for all pupils to be able to access a more local school.
No other primary schools in the city would be affected by the catchment area proposals.
The consultation on changes to the county’s admission policy ends on December 28.
The new primary is part of plans to create hundreds of new school places in Winchester at a cost of £10m.
There are also proposed plans to expand St Peter’s Catholic Primary and Winnall.